Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-31T19:40:03.441Z Has data issue: false hasContentIssue false
  • English
  • Français

On a nonlinear eigenvalue problem occurring in population genetics

Published online by Cambridge University Press:  14 November 2011

Ph. Clément  and
L. A. Peletier
Ph. Clément
Affiliation:
Delft University of Technology, Delft, The Netherlands
L. A. Peletier
Affiliation:
University of Leiden, Leiden, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Synopsis

We discuss the nonlinear eigenvalue problem

with r(–×) = –r(×) and r'≧0.

For ε = h =0, the solution to Problem P is wellknown, and every solution, except u = 0 and u =1, is unstable with respect to the corresponding parabolic problem.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 85 - 101
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Chafee, N.. Asymptotic behaviour for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary condititons. J. Differential Equations 18 (1975), 111–134.CrossRefGoogle Scholar
2Clément, Ph. and Peletier, L. A.. An anti-maximum principle for second-order elliptic operators. J. Differential Equations 34 (1979), 218–229.CrossRefGoogle Scholar
3Ewer, J. P. G. and Peletier, L. A.. On the asymptotic behaviour of solutions of semilinear parabolic equations. SIAM J. Appl. Math. 28 (1975), 43–53.CrossRefGoogle Scholar
4Fife, P. C. and Peletier, L. A.. Nonlinear diffusion in population genetics. Arch. Rational Mech. Anal. 64 (1977), 93–109.CrossRefGoogle Scholar
5Matano, H.. Asymptotic behaviour and stability of solutions of semilinear diffusion equations. Publ. Res. Inst. Math. Sci. 15 (1979), 401–454.CrossRefGoogle Scholar
6Nagylaki, T.. Conditions for the existence of clines. Genetics 80 (1975), 595–615.CrossRefGoogle ScholarPubMed
7Peletier, L. A.. On a nonlinear diffusion equation arising in population genetics. Proc. 4th Conference on ordinary and partial differential equations at Dundee. Lecture Notes in Mathematics 564, 365–371 (Berlin: Springer, 1976).Google Scholar
8Peletier, L. A.. A nonlinear eigenvalue occurring in population genetics. Proc. “Journées d'Analyse non linéaire de Besancon”. Lecture Notes in Mathematics 665, 170–187 (Berlin: Springer, 1978).Google Scholar
9Rabinowitz, P. H.. Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math. 3 (1973), 161–201.CrossRefGoogle Scholar
10Saut, J. C. and Scheurer, B.. Remarks on a nonlinear equation arising in population genetics. Comm. in P.D.E. 3 (1978), 907–931.CrossRefGoogle Scholar
11Amann, H.. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976), 620–709.CrossRefGoogle Scholar